Question: Complete the equation of the line through $(-9,7)$ and $(-6,-3)$. Use exact numbers. $y=$
Let's find the slope: $\begin{aligned} \text{Slope}&=\dfrac{-3-7}{-6-(-9)} \\\\ &=\dfrac{-10}{3} \\\\ &=-\dfrac{10}{3} \end{aligned}$ The equation is $y=-\dfrac{10}{3}x+b$ for some $b$. Let's plug the point $({-9},{7})$ to find $b$ : $\begin{aligned} y&=-\dfrac{10}{3} x+b \\\\ {7}&=-\dfrac{10}{3}({-9})+b \\\\ 7&=30+b \\\\ -23&=b \end{aligned}$ The equation is $y=-\dfrac{10}{3}x -23$.